Structural Frustration Research Articles

Metallic Bonding in Close-Packed Structures: Structural Frustration from a Hidden Gauge Symmetry

Metallic Bonding in Close-Packed Structures: Structural Frustration from a Hidden Gauge Symmetry

Investigation of structural frustration in symmetric diblock copolymers confined in polar discs through cell dynamic simulation

Nanotechnology has opened new avenues for advanced research in various fields of soft materials. Materials scientists, chemists, physicists, and computational mathematicians have begun to take a keen interest in soft materials due to their potential applications in nanopatterning, membrane separation, drug delivery, nanolithography, advanced storage media, and nanorobotics. The unique properties of soft materials, particularly self-assembly, have made them useful in fields ranging from nanotechnology to biomedicine. The discovery of new morphologies in the diblock copolymer system in curved geometries is a challenging problem for mathematicians and theoretical scientists. Structural frustration under the effects of confinement in the system helps predict new structures. This mathematical study evaluates the effects of confinement and curvature on symmetric diblock copolymer melt using a cell dynamic simulation model. New patterns in lamella morphologies are predicted. The Laplacian involved in the cell dynamic simulation model is approximated by generating a 17-point stencil discretized to a polar grid by the finite difference method. Codes are programmed in FORTRAN to run the simulation, and IBM open DX is used to visualize the results. Comparison of computational results with existing studies validates this study and identifies defects and new patterns.

Deposition of highly crystalline AlScN thin films using synchronized high-power impulse magnetron sputtering: From combinatorial screening to piezoelectric devices

With the integration of 5G in day-to-day devices and the foreseeable 6G revolution, demand for advanced radio frequency (RF) microelectromechanical systems (MEMS) is growing. Aluminum scandium nitride (AlScN) has emerged as the material of choice for many of those applications due to its superior piezoelectric and electromechanical properties compared to aluminum nitride (AlN). However, synthesizing high-quality, textured AlScN thin films is challenging. Alloying of Sc in AlN induces structural frustration leading to strain, defects, disoriented grains, and disrupted crystal symmetry during growth. Higher deposition temperatures, while improving crystalline quality, risk undesirable phase precipitation and limit industrial sustainability. In addition, future MEMS technologies also demand conformal and textured coatings over diverse topographies. Addressing these challenges collectively requires new and innovative synthesis approaches. In this study, we investigate the feasibility of ionized physical vapor deposition to deposit highly oriented AlScN films with minimal defects at lower temperatures. To this end, we employ combinations of different deposition approaches, such as metal-ion synchronized (MIS) high-power impulse magnetron sputtering (HiPIMS). Leveraging the high ionization rates of HiPIMS and optimally timed substrate bias potentials, we selectively bombard the growing film with Al and/or Sc ions to enhance the adatom mobility at low temperatures while simultaneously providing the ability to tune stress and coat complex structures conformally. The nonequilibrium solubility of Sc in wurtzite AlN under different conditions is investigated using a combinatorial deposition approach. Promising candidates with ∼20% Sc composition are isolated and characterized for crystallinity and residual stress. Disoriented grains, a significant issue in growing AlScN films, are observed through atomic force microscopy and found to be completely removed by substrate rotation and application of substrate biasing. The measured piezoelectric response of the films with approximately 20% Sc concentration ranges from 6.3 to 8.8 pm/V, in line with density functional theory predictions and experimentally reported values for films deposited in a production tool with coplanar geometry. At the same time, MIS-HiPIMS-deposited films offer unique properties and flexibility to tune their stress state and structural properties, thus presenting exciting opportunities for the fabrication of advanced RF filters and next-generation MEMS devices. Published by the American Physical Society 2024

Elasticity of self-organized frustrated disordered spring networks.

There have been some interesting recent advances in understanding the notion of mechanical disorder in structural glasses and the statistical mechanics of these systems' low-energy excitations. Here we contribute to these advances by studying a minimal model for structural glasses' elasticity in which the degree of mechanical disorder-as characterized by recently introduced dimensionless quantifiers-is readily tunable over a very large range. We comprehensively investigate a number of scaling laws observed for various macro, meso and microscopic elastic properties, and rationalize them using scaling arguments. Interestingly, we demonstrate that the model features the universal quartic glassy vibrational density of states as seen in many atomistic and molecular models of structural glasses formed by cooling a melt. The emergence of this universal glassy spectrum highlights the role of self-organization (toward mechanical equilibrium) in its formation, and elucidates why models featuring structural frustration alone do not feature the same universal glassy spectrum. Finally, we discuss relations to existing work in the context of strain stiffening of elastic networks and of low-energy excitations in structural glasses, in addition to future research directions.

Patterns of Nanoporous Spherical Packing Emerging under Influence of Curvature and Confinement

Nanoporous membranes are popular in nanotechnology due to biomedical and industrial applications. During the past decade, experimental, theoretical and computational research into porous membranes and soft materials has opened up new mathematical dimensions. In bulk, diblock copolymers exhibit ordered morphologies such as parallel matrices of lamellae, bicontinuous matrices of gyroids, hexagonal matrices of cylinders and body-centred cubic matrices of spheres. In melt, confinement plays an essential role in tuning the frustration of the diblock copolymer system to predict more nanostructures. These nanostructures depend on the composition of the copolymers, their confining geometries and the degree of structural frustration. An isotropic 9-point stencil for Laplacian is constructed. The discrete finite-difference technique is used in polar grids to discretize the macromolecule of the diblock copolymer system to study spherical patterns to study the effect of curvature and confinement with a well-known and efficient cell dynamic simulation model. Intel FORTRAN (IFORT) codes are generated to run the CDS model and visualisation of simulation results is observed with the help of OPENDX. A comparison of the proposed study with existing experimental and computational studies is also presented.

Monte Carlo simulation of the planar discrete double layer for neutrally charged interfaces

A Monte Carlo simulation study on the charge distribution and structure of the electric double layer (EDL) that forms between two planar interfaces is presented, using a model electrolyte of monovalent hard-sphere ions and confining walls composed of two discrete and sign-alternating charge distributions. Symmetric and asymmetric plate-plate orientations, along with uncharged walls, are considered. Results are presented for effective wall-ion correlation functions and local integrated charge in the subvolumes defined by the charge domains on the plates. We report that, in the presence of multifaceted charged surfaces, the ions between the walls exhibit complex and rich behavior, with the formation of an EDL next to the charged domains of the interface, and having density profiles of counterions and coions that are established as function of the nature and configuration of the charged strips. These profiles present a structural frustration that renders the subvolumes with a net charge, in contrast to the null net charge from profiles next to a uniformly charged surface. Finally, with proper scaling, the integrated charge follows closely a master curve for each wall-wall configuration. Such phenomenology is visible in the regime of low and high surface charge.

Observation of atomically displacive transformation out of the boundary-reconstructive phase competition

During the phase transitions, diverse states evolve with multiplex phenomena arising from the critical competition. In this study, a displacive martensitic transformation with a lattice shear distortion was unexpectedly observed at the reconstructive phase boundary that usually connects multiple phases without crystallographic relation, in a Ni–Co–Mn–V all-d-metal Heusler alloy system. Experiments and theoretical calculations suggest that the parent phase becomes increasingly unstable when approaching the phase boundary. The lattice-distorted transformation with moderate first-order nature survives due to the critical phase competition from the structural frustration, in which the comparable energy and the diminished formation preference of different phases emerge. In this critical state, the phase selection including the martensitic transformation can be tuned by external fields such as rapid cooling, annealing, and magnetic field. Our research reveals a novel manner to destabilize the parent phase, through which one could attain new functional materials based on the phase transitions.

Robust and Accessible True Random Number Generator Exploiting the Structural Frustration of Nematic Liquid Crystals

AbstractThe study proposes a highly credible true random number generator based on the structural frustration of nematic liquid crystals, which refers to the appearance of two energetically equivalent structures in a nematic system. Frustration is induced in a simple liquid crystal cell by applying an electric field and observing optical textures under crossed polarizers. A clockwise or counterclockwise spiral image appears on 630 separate circular electrodes under the electric field, and random binary sequences are obtained by assigning a digit of 0 or 1 to each image. These sequences pass the strict statistical randomness tests of the National Institute of Standards and Technology with a pass rate of 0.992 or higher for the ten applicable tests and exhibit excellent uniformity. Furthermore, a simple method is introduced to convert the binary results to random decimal numbers with only a minimal amount of data processing.

Correlation of the chemical composition, phase content, structural characteristics and magnetic properties of the Bi-substituted M-type hexaferrites

Bi-substituted M-type hexaferrites, BaFe12-xBixO19 (0.1 ≤ x ≤ 1.2), or Bi-BaM, were produced by the solid-state reactions. The correlation between the phase content, chemical composition, crystal structure features, and peculiarities of the magnetic properties of Bi-BaM was established using XRD (X-ray diffraction), SEM (scanning electron microscopy), and VSM (vibrational sample magnetometry). XRD phase analysis made it possible to establish the limit of substitution of Fe3+ ions by Bi3+ ions. It was shown that at a low substitution level (x ≤ 0.3), no impurity phases were detected, and the samples are characterized by a single-phase state with the space group (SG) P63/mmc. As the degree of substitution (x ≥ 0.6) increases, the formation of impurity phases was observed, which can be explained by the difficulties of ion diffusion in the process of solid-phase synthesis as well as the formation of defects in the magnetoplumbite structure due to the large ionic radius of Bi3+. As impurity phases in the studied compositions (x ≥ 0.6) the following were noted: BiFeO3 (SG: Pnma); BiO2 (SG: Fm-3m); BaBi2O6 (SG: R-3); and Ba0.5Bi1.5O2.16 (SG: Im-3m). The content of the main phase (SG: P63/mmc) decreases from 95.11 to 88.27 vol% with an increase in x from 0.6 to 1.2, respectively. Analysis of SEM images showed the growth of particles up to 10 μm, depending on the concentration of bismuth oxide during hexaferrite synthase. The Bi-BaM magnetic characteristics were examined using VSM in the range of 3 T at 300 K. Due to the magnetic structure's frustration, with increased x a decrease in saturation magnetization (Ms) was found. There were two concentration diapasons with different speeds of Ms decrease. In the first diapason, the main contribution belong to the magnetic structure frustration in the frame of the main phase (P63/mmc) due to the long-range Fe-O-Fe exchange interaction weakening (under Bi substitution). In the second diapason, the main contribution belong to the impurity phase formation and decrease of the main magnetic phase concentration in samples.

A Dynamic Triradical: Synthesis, Crystal Structure, and Spin Frustration.

Polyradicals, i.e., multispin organic molecules, are playing important roles in radical-based material applications for their spin-spin interaction. A dynamic covalently bonded multispin molecule may endow materials with added function such as memory and switching. However, such a species has yet to be reported. We here report the synthesis, characterization, and crystal structure of a dynamic triradical species. It is generated by the self-assembly of two molecules through a Lewis acid coupled electron transfer. The crystalline species is spin-frustrated without Jahn-Teller distortion at low temperature, while it dissociates back to diamagnetic starting material in solution at high temperature. The reversible process is tracked by variable-temperature NMR, EPR, and UV-vis-NIR spectroscopy. Isolation, property study, and dynamic bonding investigation on such a species lay the foundation for the design of functional polyradicals with potential application as memory or switching devices.

High entropy BaFe12-x(Ti/Mn/Ga/In)xO19 (x = 1–7) oxides: Correlation of the composition, entropy state, magnetic characteristics, and terahertz properties

The BaFe12-x (Ti/Mn/Ga/In)xO19 (x = 1–7) high-entropy oxides (HEOs) were obtained by solid-phase synthesis. The correlation of the chemical composition (the level of the Fe replacement), structural parameters, magnetic characteristics, and terahertz (THz) properties was investigated. All studied samples were single-phase (SG: P63/mmc). Lattice parameters showed a monotonic increasing trend with an increase of (x). The key role in increasing the lattice parameters of HEOs may belong to the influence of In3+ ions, which are much larger in size than Fe3+ ions. As one of the possible reason for explanation of the lattice parameters behavior we hypothesized that partial charge transformation of the Mn3+ state to the Mn2+ state takes place in order to maintain electrical neutrality. Other cations (Ti/Ga/In) have stable oxidation state. The anisotropic nature of the increase in lattice parameters was demonstrated. No strong correlation between chemical composition and microstructural parameters of the investigated HEOs was observed. The magnetic characteristics of the BaFe12-x (Ti/Mn/Ga/In)xO19 (x = 1–7) HEOs were investigated at broad intervals of magnetic fields and temperatures. The behavior of the magnetic characteristics was shown to be the result of the magnetic structure frustration. In addition, terahertz electrodynamic properties were studied by measuring spectra of complex dielectric permittivity at frequencies 0.2–1.2 THz in the temperature interval 20–300 K. The spectra indicate the presence of a higher-frequency infrared phonon resonance, whose damping decreases with cooling, as well as an excitation below 0.2 THz that freezes out at low temperatures, the origin of which is associated with the polycrystalline nature of the materials.

Analysis of Structural Change across the Liquid-Liquid Transition and the Widom Line in Supercooled Stillinger-Weber Silicon.

We consider the changes in the structure of supercooled Stillinger-Weber silicon at pressures at which the studied range of temperatures traverses the liquid-liquid transition or the "Widom line" (at which the isothermal compressibility or the specific heat exhibits a maximum). In addition to the conventional characterizations in terms of the pair-correlation function and bond orientational order, we analyze the statistics of rings in the bond network as well as the statistics of clusters of low density liquid (LDL)- and high density liquid (HDL)-like atoms. We investigate the nature of the change in these structural characterizations when the liquid-liquid transition line or the Widom line is crossed. We find that the isobaric temperature variation of these structural features reveals clear indications of maximal structural heterogeneity or frustration upon crossing the liquid-liquid transition or the Widom line, as in the case of water, but with some differences in detail, which we discuss.

Disulfide-Bond-Induced Structural Frustration and Dynamic Disorder in a Peroxiredoxin from MAS NMR.

Disulfide bond formation is fundamentally important for protein structure and constitutes a key mechanism by which cells regulate the intracellular oxidation state. Peroxiredoxins (PRDXs) eliminate reactive oxygen species such as hydrogen peroxide through a catalytic cycle of Cys oxidation and reduction. Additionally, upon Cys oxidation PRDXs undergo extensive conformational rearrangements that may underlie their presently structurally poorly defined functions as molecular chaperones. Rearrangements include high molecular-weight oligomerization, the dynamics of which are, however, poorly understood, as is the impact of disulfide bond formation on these properties. Here we show that formation of disulfide bonds along the catalytic cycle induces extensive μs time scale dynamics, as monitored by magic-angle spinning NMR of the 216 kDa-large Tsa1 decameric assembly and solution-NMR of a designed dimeric mutant. We ascribe the conformational dynamics to structural frustration, resulting from conflicts between the disulfide-constrained reduction of mobility and the desire to fulfill other favorable contacts.

Magnetic Breakdown and Topology in the Kagome Superconductor CsV_{3}Sb_{5} under High Magnetic Field.

The recently discovered layered kagome metals of composition AV_{3}Sb_{5} (A=K, Rb, Cs) exhibit a complex interplay among superconductivity, charge density wave order, topologically nontrivial electronic band structure and geometrical frustration. Here, we probe the electronic band structure underlying these exotic correlated electronic states in CsV_{3}Sb_{5} with quantum oscillation measurements in pulsed fields up to 86T. The high-field data reveal a sequence of magnetic breakdown orbits that allows the construction of a model for the folded Fermi surface of CsV_{3}Sb_{5}. The dominant features are large triangular Fermi surface sheets that cover almost half the folded Brillouin zone. These sheets have not yet been detected in angle resolved photoemission spectroscopy and display pronounced nesting. The Berry phases of the electron orbits have been deduced from Landau level fan diagrams near the quantum limit without the need for extrapolations, thereby unambiguously establishing the nontrivial topological character of several electron bands in this kagome lattice superconductor.

Dynamically tunable lamellar surface structures from magnetoactive elastomers driven by a uniform magnetic field.

Stimuli responsive materials are key ingredients for any application that requires dynamically tunable or on-demand responses. In this work we report experimental and theoretical investigation of magnetic-field driven modifications of soft-magnetic elastomers whose surface was processed by laser ablation into lamellar microstructures that can be manipulated by a uniform magnetic field. We present a minimal hybrid model that elucidates the associated deflection process of the lamellae and explains the lamellar structure frustration in terms of dipolar magnetic forces arising from the neighbouring lamellae. We experimentally determine the magnitude of the deflection as a function of magnetic flux density and explore the dynamic response of lamellae to fast changes in a magnetic field. A relationship between the deflection of lamellae and modifications of the optical reflectance of the lamellar structures is resolved.

Nanospheres with Patches Arranged in Polyhedrons from Self-Assembly of Solution-State Diblock Copolymers under Spherical Confinement

Self-assembly of sphere-forming solution-state amphiphilic diblock copolymers under spherical nanopore confinement is investigated using a simulated annealing technique. For two types of cases of different pore–surface/copolymer interactions, sequences of self-assembled patchy nanospheres are obtained, and phase diagrams are constructed. Self-assembled patchy nanospheres with 1–21 solvophobic domains are observed. The outermost solvophobic domains (patches) are packed into various polyhedrons when their number is larger than 3, where three Platonic solids of a regular tetrahedron, an octahedron, and an icosahedron and seven Johnson solids of J12, J13, J17, J50, J51, J86, and J87 are identified. In addition, another Johnson solid of J84 is identified in a structure with two categories of B-domains. These polyhedrons have all or most of their faces in a triangular shape, and hence, they are closer to spherical in shape, which may relieve the chain stretching. Nanospheres with 1, 4, 6, 9, and 12 numbers of patches occur in relatively large windows in the phase diagrams of both types of cases. In one of the two types of cases, all nanospheres with any number of 1–14 patches occur in the phase diagram, whereas in the other type of cases, nanospheres with 2, 3, 5, 11, and 13 numbers of patches are absent in the phase diagram. Furthermore, at a given pore size, the number of patches changes nonmonotonically or is unchanged with an increase in the strength of the pore–surface/copolymer interactions for one type or the other type of case, respectively. Quantitative calculations are performed to elucidate mechanisms of the window size in the phase diagrams of nanospheres with different numbers of patches and structure details. All the observed phase behaviors can be well-explained based on the structure frustration, the conclusion being that the systems tend to avoid forming polyhedral structures with uneven distribution of solvophobic domains, and the differences between the two types of cases. Our results may provide a fundamental understanding of the relationship among confinement conditions, solvent conditions, and self-assembled structures.

Engineering the Morphologies of Block Copolymer Particles from the Confined Self‐assembly within Emulsion Droplets†

Comprehensive SummaryBlock copolymers (BCPs) can automatically assemble into various regulated nanoparticles when they are confined within the emulsion droplet because of the structural frustration of polymer chains and the soft template effect of the oil/water interface. In the past few years, great efforts have been made to regulate the morphologies of the resulting BCP particles. In this review article, various strategies for tuning oil/water interfacial properties to engineer the as‐formed BCP particles were summarized. Then, the comprehensive scenarios of the applications of the resulting BCP particles were discussed. Finally, the future tendency and challenge of the self‐assembly of BCPs confined in emulsion droplet were suggested.

Confined Self-Assembly of Block Copolymers within Emulsion Droplets: A Perspective.

When the self-assembly of block copolymers (BCPs) occurs within organic emulsion droplets in the aqueous phase, the strong structural frustration of BCP chains causes the formation of a series of well-regulated BCP particles that cannot be obtained from the self-assembly of BCPs in the bulk state or solution. In this Perspective, we review the recent progress of the self-assembly of BCPs confined in emulsion droplets. The governing factors of the structure and morphology of the as-prepared BCP particles are summarized. In addition, the applications of the as-prepared BCP particles in photonic crystals and drug release are discussed. Finally, we also give a forward-looking perspective on future challenges in this field.

Mechanism of temperature-induced asymmetric swelling and shrinking kinetics in self-healing hydrogels

Understanding the physical principle that governs the stimuli-induced swelling and shrinking kinetics of hydrogels is indispensable for their applications. Here, we show that the shrinking and swelling kinetics of self-healing hydrogels could be intrinsically asymmetric. The structure frustration, formed by the large difference in the heat and solvent diffusions, remarkably slows down the shrinking kinetics. The plateau modulus of viscoelastic gels is found to be a key parameter governing the formation of structure frustration and, in turn, the asymmetric swelling and shrinking kinetics. This work provides fundamental understandings on the temperature-triggered transient structure formation in self-healing hydrogels. Our findings will find broad use in diverse applications of self-healing hydrogels, where cooperative diffusion of water and gel network is involved. Our findings should also give insight into the molecular diffusion in biological systems that possess macromolecular crowding environments similar to self-healing hydrogels.

The Structural Rule Distinguishing a Superfold: A Case Study of Ferredoxin Fold and the Reverse Ferredoxin Fold.

Superfolds are folds commonly observed among evolutionarily unrelated multiple superfamilies of proteins. Since discovering superfolds almost two decades ago, structural rules distinguishing superfolds from the other ordinary folds have been explored but remained elusive. Here, we analyzed a typical superfold, the ferredoxin fold, and the fold which reverses the N to C terminus direction from the ferredoxin fold as a case study to find the rule to distinguish superfolds from the other folds. Though all the known structural characteristics for superfolds apply to both the ferredoxin fold and the reverse ferredoxin fold, the reverse fold has been found only in a single superfamily. The database analyses in the present study revealed the structural preferences of - and -units; the preferences separate two -helices in the ferredoxin fold, preventing their collision and stabilizing the fold. In contrast, in the reverse ferredoxin fold, the preferences bring two helices near each other, inducing structural conflict. The Rosetta folding simulations suggested that the ferredoxin fold is physically much more realizable than the reverse ferredoxin fold. Therefore, we propose that minimal structural conflict or minimal frustration among secondary structures is the rule to distinguish a superfold from ordinary folds. Intriguingly, the database analyses revealed that a most stringent structural rule in proteins, the right-handedness of the -unit, is broken in a set of structures to prevent the frustration, suggesting the proposed rule of minimum frustration among secondary structural units is comparably strong as the right-handedness rule of the -unit.